The bearing capacity factor N gamma of strip footings on c- gamma soil using the method of characteristics

• Published in: SpringerPlus Vol. 5; no. 1; pp. 1 - 17
• Main Authors: Han, Dongdong, Xie, Xinyu, Zheng, Lingwei, Huang, Li
• Format: Journal Article
• Language: English
• Published: 01.12.2016
• ISSN: 2193-1801
• DOI: 10.1186/s40064-016-3084-6

The method of characteristics (also called as the slip-line method) is used to calculate the bearing capacity of strip footings on ponderable soil. The soil is assumed to be a rigid plastic that conforms to the Mohr-Coulomb criterion. The solution procedures proposed in this paper is implemented using a finite difference method and suitable for both smooth and rough footings. By accounting for the influence of the cohesion c, the friction angle and the unit weight gamma of the soil in one failure mechanism, the solution can strictly satisfy the required boundary conditions. The numerical solution of N gamma are consistent with published complete solutions based on cohesionless soil with no surcharge load. The relationship of N gamma between smooth and rough foundations is discussed which indicates that the value of N gamma for a smooth footing is only half or more of that for a rough footing. The influence of lambda ( lambda = (q + ccot )/ gamma B) on N gamma is studied. Finally, a curve-fitting formula that simultaneously considers both and lambda is proposed and is used to produce a series of N gamma versus lambda curves. The surcharge ratio lambda and roughness of the footing base both have significant impacts on N gamma . The formula for the bearing capacity on c- gamma soil can be still expressed by Terzaghi's equation except that the bearing capacity factor N gamma depends on the surcharge ratio lambda in addition to the friction angle. Comparisons with the exact solutions obtained from numerical results indicate that the proposed formula is able to provide an accurate approximation with an error of no more than plus or minus 2 %.